Host rocks and country rocks are well defined technical terms in geology.
A host rock is older than the rock body and deposit introduced into it, or in other words it serves as a host to gold deposits.
The term country rock is less specific and does not tell you anything about the age relation between the Au deposit and its surrounding rocks. It only describes a spatial relationship but not a chronological one.
The simple answer is one has gold and the other doesn't. But you need to understand the processes involved in concentrating the gold to define the differences and hence what to look for in the exploration programme.
Country rock, such as a Bouma Sequence, will have rocks which can react with the fluids and deposit gold in different forms.
Greywackes will have tangential or axial planar veins with coarse gold with low Sulphide and Carbonate and associated Te, Bi, Ag, Pb and Zn and be of limited tonnes.
The shales will be the locus of lode style large tonnage deposits spreading from the axial planar joints and be high S and rich in arsenic and Cu.
The active minerals are sources of Ca, (Ca Feldspars and amphiboles) to drive carbonation then Sulphurisation of Fe++ in Magnetite, Pyrrhotite, Chlorite and Grunerite to drop the gold and increase the pH.
The presence of quartz vein in porphyries with hydrothermal biotite-orthoclase was an encouraging sign for gold mineralization. That was in Archean porphyries (volcanic origin probably) of the Abitibi Belt, but this would be similar in other ages/locations.